Found:

internal domain

SYNTAX: Notion in checking theory. The internal domain of A is the minimal complement domain of A. EXAMPLE: In (i), the complement domain of X (and H) is YP and everything YP dominates. The internal domain of X (and H) is just YP.

(i)    XP1
       /\
      /  \
     UP  XP2
        /\
       /  \
     ZP1    X'
    /\      /\
   /  \    /  \
  WP  ZP2  X1  YP
          /\
         /  \
        H   X2